If you were investing $100,000 in someone, would you want them to leave before you've gotten a return on your investment?

As an employee, you're an investment. A company will invest money in training/paying you, and you give them a return by contributing value to them.

In my mind, as you look for a job, the more you can adjust your approach to match the needs of the employer, the more likely you are to succeed in the hiring process.

To your question, the answer really depends on what the companies needs are, but generally my advice would be to leave the second job off your resume.

The reason is that it will generally reflect negatively on you more then it will help you.

But you're not off the hook yet. At some point in the hiring process, they might ask you for your full employment history. It could be as early as the application stating "list your three most recent employers" or as late as a background check once you've gotten an offer.

Let them ask YOU about it. Then you can explain. Don't put it on your resume, but don't lie about it in your application either. Just focus on how you're going to bring value to their organization.